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Abstract:

In this paper we study the existence of nontrivial solutions of the problem {-Δu+u = u p-2u in Ω, {∂u/∂v = λ u q-2u on ∂Ω, with 1<q<2(N-1)/(N-2) and 1<p≤2N/(N-2). In the concave-convex case, i.e., 1<q<2<p, if λ is small there exist two positive solutions while for λ large there is no positive solution. When p is critical, and q subcritical we obtain existence results using the concentration compactness method. Finally, we apply the implicit function theorem to obtain solutions for λ small near u0 = 1. © 2003 Elsevier Science (USA). All rights reserved.

Registro:

Documento: Artículo
Título:A convex-concave problem with a nonlinear boundary condition
Autor:Garcia-Azorero, J.; Peral, I.; Rossi, J.D.
Filiación:Departamento de Matemáticas, U. Autonoma de Madrid, Ctra. de Colmenar Km 15, 28049 Madrid, Spain
Departamento de Matemt́ica, FCEyN UBA, 1428 Buenos Aires, Argentina
Palabras clave:Critical exponents; Nonlinear boundary conditions
Año:2004
Volumen:198
Número:1
Página de inicio:91
Página de fin:128
DOI: http://dx.doi.org/10.1016/S0022-0396(03)00068-8
Título revista:Journal of Differential Equations
Título revista abreviado:J. Differ. Equ.
ISSN:00220396
CODEN:JDEQA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00220396_v198_n1_p91_GarciaAzorero.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v198_n1_p91_GarciaAzorero

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Citas:

---------- APA ----------
Garcia-Azorero, J., Peral, I. & Rossi, J.D. (2004) . A convex-concave problem with a nonlinear boundary condition. Journal of Differential Equations, 198(1), 91-128.
http://dx.doi.org/10.1016/S0022-0396(03)00068-8
---------- CHICAGO ----------
Garcia-Azorero, J., Peral, I., Rossi, J.D. "A convex-concave problem with a nonlinear boundary condition" . Journal of Differential Equations 198, no. 1 (2004) : 91-128.
http://dx.doi.org/10.1016/S0022-0396(03)00068-8
---------- MLA ----------
Garcia-Azorero, J., Peral, I., Rossi, J.D. "A convex-concave problem with a nonlinear boundary condition" . Journal of Differential Equations, vol. 198, no. 1, 2004, pp. 91-128.
http://dx.doi.org/10.1016/S0022-0396(03)00068-8
---------- VANCOUVER ----------
Garcia-Azorero, J., Peral, I., Rossi, J.D. A convex-concave problem with a nonlinear boundary condition. J. Differ. Equ. 2004;198(1):91-128.
http://dx.doi.org/10.1016/S0022-0396(03)00068-8